Finite Group Databasebeta

← C31×#25553 #21482312

Subgroups — C31×#25553 #21482312

Order 7936.

1200 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#553C211yesmaximal, characteristic, complemented
2C2×C31×#480C211yesmaximal, characteristic, complemented
3C2×C31×#469C211yesmaximal, characteristic, complemented
4C31×#2414C211yesmaximal, characteristic, complemented
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2033C211yesmaximal, characteristic, complemented
7C31×#2025C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic, complemented
9C31×#1879C211yesmaximal, characteristic, complemented
10C31×#1875C211yesmaximal, characteristic, complemented
11C31×#1875C211yesmaximal, characteristic, complemented
12C31×#1870C211yesmaximal, characteristic, complemented
13C31×#1862C211yesmaximal, characteristic, complemented
14C31×#1854C211yesmaximal, characteristic, complemented
15C31×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C31×#553—24no—
19C31×#553—24no—
20C2×C31×#126—21no—
21C2×C31×#125C2211yescharacteristic
22C2×C31×#123—21no—
23C2×C31×#121—21no—
24C2×C31×#121C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C4×D4×C31—21no—
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#117C2211yescharacteristic
32C2×C31×#117C2211yescharacteristic
33C22×C4⋊C4×C31C2211yescharacteristic
34C31×#480—24no—
35C31×#469—24no—
36C2×C31×#107C2211yescharacteristic
37C2×C31×#107C2211yescharacteristic
38C2×C31×#106C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C31×#394—21no—
49C31×#392—21no—
50C31×#390—21no—
51C31×#390C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#388—21no—
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31D411yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C22×D4×C31C2311yescharacteristic
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C2×D8×C31—22no—
75C2×D8×C31—22no—
76C2×D8×C31—41no—
77C2×M16×C31—22no—
78C2×M16×C31—22no—
79C2×M16×C31—41no—
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C31×#126—28no—
85C31×#125—22no—
86C31×#125—22no—
87C31×#123—28no—
88C31×#121—28no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—22no—
95C31×#121—41no—
96C31×#121D414yescomplemented
97C4×D4×C31—28no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C31×#117—22no—
103C31×#117—22no—
104C31×#117—22no—
105C31×#117—41no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31D414yescomplemented
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31D411yescharacteristic
130C2×C22⋊C4×C31D411yescharacteristic
131C2×C42×C31—21no—
132C2×C42×C31—21no—
133C2×C42×C31C2311yescharacteristic
134C31×#107—22no—
135C31×#107—22no—
136C31×#106—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—41no—
143C31×C22⋊C8—22no—
144C31×C22⋊C8—22no—
145C31×C22⋊C8—41no—
146C31×#95—21no—
147C31×#95—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31C2×D411yescharacteristic
151C24×C31C2×D411yescharacteristic
152C2×D4×C31—22no—
153C2×D4×C31—24no—
154C2×D4×C31—24no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—41no—
167C2×D4×C31—41no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31—81no—
174C2×D4×C31—81no—
175C2×D4×C31—81no—
176C2×D4×C31—81no—
177C2×D4×C31—81no—
178C2×D4×C31C2×D412yes—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—24no—
188C22×C4×C31—24no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—81no—
198C22×C4×C31—81no—
199C22×C4×C31—81no—
200C22×C4×C31—81no—
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D412yes—
206C22×C4×C31C2×D412yes—
207C22×C4×C31C2411yescharacteristic
208D8×C31—44no—
209M16×C31—44no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31#4112yes—
222C4⋊C4×C31—24no—
223C4⋊C4×C31—24no—
224C4⋊C4×C31—24no—
225C4⋊C4×C31—22no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—81no—
235C4⋊C4×C31C2×D412yes—
236C4⋊C4×C31C2×D412yes—
237C4⋊C4×C31C2×D412yes—
238C4⋊C4×C31#4112yes—
239C22⋊C4×C31—24no—
240C22⋊C4×C31—24no—
241C22⋊C4×C31—24no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—24no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C22⋊C4×C31—42no—
248C22⋊C4×C31—42no—
249C22⋊C4×C31—81no—
250C22⋊C4×C31—81no—
251C42×C31—24no—
252C42×C31—21no—
253C42×C31—21no—
254C42×C31—42no—
255#25553C3111yesmaximal, characteristic, direct product factor, Sylow
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—22no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31#12012yes—
284C23×C31C22×D411yescharacteristic
285D4×C31—22no—
286D4×C31—22no—
287D4×C31—44no—
288D4×C31—48no—
289D4×C31—41no—
290D4×C31—41no—
291D4×C31—41no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—41no—
295D4×C31—84no—
296D4×C31—84no—
297D4×C31—84no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—22no—
307C2×C4×C31—21no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—84no—
336C2×C4×C31—84no—
337C2×C4×C31#12012yes—
338C2×C4×C31C22×D411yescharacteristic
339C2×C4×C31C22×D411yescharacteristic
340C2×C4×C31C2×#4111yescharacteristic
341C2×C4×C31C2×#4111yescharacteristic
342C2×C4×C31H(5,𝔽2)11yescharacteristic
343C2×C4×C312−1+411yescharacteristic
344C8×C31—22no—
345C8×C31—41no—
346C8×C31—41no—
347C8×C31—41no—
348C2×#553C2×C3111yescharacteristic, complemented
349C2×#480C2×C3111yescharacteristic, complemented
350C2×#469C2×C3111yescharacteristic, complemented
351#2414C2×C3111yescharacteristic, complemented
352#2059C2×C3111yescharacteristic, complemented
353#2033C2×C3111yescharacteristic, complemented
354#2025C2×C3111yescharacteristic, complemented
355#1999C2×C3111yescharacteristic, complemented
356#1879C2×C3111yescharacteristic, complemented
357#1875C2×C3111yescharacteristic, complemented
358#1875C2×C3111yescharacteristic, complemented
359#1870C2×C3111yescharacteristic, complemented
360#1862C2×C3111yescharacteristic, complemented
361#1854C2×C3111yescharacteristic, complemented
362#1736C2×C3111yescharacteristic, complemented
363C22×C31—22no—
364C22×C31—22no—
365C22×C31—22no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—42no—
374C22×C31—41no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—41no—
378C22×C31—41no—
379C22×C31—41no—
380C22×C31—81no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31—81no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31C2×#12011yescharacteristic
392C22×C31#54611yescharacteristic
393C22×C31#54711yescharacteristic
394C22×C31#57511yescharacteristic
395C22×C31#57511yescharacteristic
396C22×C31#57611yescharacteristic
397C22×C31#57611yescharacteristic
398C4×C31—22no—
399C4×C31—41no—
400C4×C31—41no—
401C4×C31—42no—
402C4×C31—41no—
403C4×C31—42no—
404C4×C31—42no—
405C4×C31—42no—
406C4×C31—81no—
407C4×C31—81no—
408C4×C31#53211yescharacteristic
409C4×C31#53711yescharacteristic
410C4×C31#54611yescharacteristic
411C4×C31#54711yescharacteristic
412C22×D8C22×C3111yescharacteristic
413C22×M16C22×C3111yescharacteristic
414#553—24no—
415#553—24no—
416C2×#126—21no—
417C2×#125C22×C3111yescharacteristic
418C2×#123—21no—
419C2×#121—21no—
420C2×#121C22×C3111yescharacteristic
421C2×#121C22×C3111yescharacteristic
422C2×#121C22×C3111yescharacteristic
423C2×#121C22×C3111yescharacteristic
424C2×C4×D4—21no—
425C2×C4×D4C22×C3111yescharacteristic
426C2×C4×D4C22×C3111yescharacteristic
427C2×#117C22×C3111yescharacteristic
428C2×#117C22×C3111yescharacteristic
429C22×C4⋊C4C22×C3111yescharacteristic
430#480—24no—
431#469—24no—
432C2×#107C22×C3111yescharacteristic
433C2×#107C22×C3111yescharacteristic
434C2×#106C22×C3111yescharacteristic
435C2×#102C22×C3111yescharacteristic
436C2×#102C22×C3111yescharacteristic
437C2×#102C22×C3111yescharacteristic
438C2×#102C22×C3111yescharacteristic
439C2×#102C22×C3111yescharacteristic
440C2×#102C22×C3111yescharacteristic
441C2×C22⋊C8C22×C3111yescharacteristic
442C2×C22⋊C8C22×C3111yescharacteristic
443C2×C22⋊C8C22×C3111yescharacteristic
444#394—21no—
445#392—21no—
446#390—21no—
447#390C22×C3111yescharacteristic
448#389C22×C3111yescharacteristic
449#388—21no—
450#380C22×C3111yescharacteristic
451#340C22×C3111yescharacteristic
452#340C22×C3111yescharacteristic
453#340C22×C3111yescharacteristic
454#340C22×C3111yescharacteristic
455#340C22×C3111yescharacteristic
456#340C22×C3111yescharacteristic
457#336C22×C3111yescharacteristic
458#336C22×C3111yescharacteristic
459C2×C31—42no—
460C2×C31—81no—
461C2×C31—82no—
462C2×C31—161no—
463C2×C31#243011yescharacteristic
464C2×C31#300511yescharacteristic
465C2×C31#300811yescharacteristic
466C2×C31#330911yescharacteristic
467C2×C31#332211yescharacteristic
468C2×C31#334711yescharacteristic
469C2×C31#335511yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4D4×C3111yescharacteristic
475C22×D4C23×C3111yescharacteristic
476C22×D4C23×C3111yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4C23×C3111yescharacteristic
480C23×C4C23×C3111yescharacteristic
481C2×D8—22no—
482C2×D8—22no—
483C2×D8—41no—
484C2×M16—22no—
485C2×M16—22no—
486C2×M16—41no—
487C22×C8C23×C3111yescharacteristic
488C22×C8C23×C3111yescharacteristic
489C22×C8C23×C3111yescharacteristic
490C22×C8C23×C3111yescharacteristic
491#126—28no—
492#125—22no—
493#125—22no—
494#123—28no—
495#121—28no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—41no—
503#121D4×C3114yescomplemented
504C4×D4—28no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509#117—22no—
510#117—22no—
511#117—22no—
512#117—41no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4D4×C3111yescharacteristic
519C2×C4⋊C4D4×C3114yescomplemented
520C2×C4⋊C4C23×C3111yescharacteristic
521C2×C4⋊C4C23×C3111yescharacteristic
522C2×C4⋊C4C23×C3111yescharacteristic
523C2×C4⋊C4C23×C3111yescharacteristic
524C2×C4⋊C4C23×C3111yescharacteristic
525C2×C4⋊C4C23×C3111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C3111yescharacteristic
537C2×C22⋊C4D4×C3111yescharacteristic
538C2×C42—21no—
539C2×C42—21no—
540C2×C42C23×C3111yescharacteristic
541#107—22no—
542#107—22no—
543#106—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—41no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—41no—
553#95—21no—
554#95—21no—
555C31#2555311yescharacteristic, direct product factor, Sylow
556C24—21no—
557C24—21no—
558C24C2×D4×C3111yescharacteristic
559C24C2×D4×C3111yescharacteristic
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4C2×D4×C3112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C3111yescharacteristic
610C22×C4C2×D4×C3111yescharacteristic
611C22×C4C2×D4×C3111yescharacteristic
612C22×C4C2×D4×C3111yescharacteristic
613C22×C4C2×D4×C3112yes—
614C22×C4C2×D4×C3112yes—
615C22×C4C24×C3111yescharacteristic
616D8—44no—
617M16—44no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8#41×C3112yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—81no—
643C4⋊C4C2×D4×C3112yes—
644C4⋊C4C2×D4×C3112yes—
645C4⋊C4C2×D4×C3112yes—
646C4⋊C4#41×C3112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42—42no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23C31×#12012yes—
691C23C22×D4×C3111yescharacteristic
692D4—22no—
693D4—22no—
694D4—44no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4C31×#12012yes—
745C2×C4C22×D4×C3111yescharacteristic
746C2×C4C22×D4×C3111yescharacteristic
747C2×C4C2×#41×C3111yescharacteristic
748C2×C4C2×#41×C3111yescharacteristic
749C2×C4C31×H(5,𝔽2)11yescharacteristic
750C2×C4C31×2−1+411yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×C31×#12011yescharacteristic
784C22C31×#54611yescharacteristic
785C22C31×#54711yescharacteristic
786C22C31×#57511yescharacteristic
787C22C31×#57511yescharacteristic
788C22C31×#57611yescharacteristic
789C22C31×#57611yescharacteristic
790C4—22no—
791C4—41no—
792C4—41no—
793C4—42no—
794C4—41no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—81no—
799C4—81no—
800C4C31×#53211yescharacteristic
801C4C31×#53711yescharacteristic
802C4C31×#54611yescharacteristic
803C4C31×#54711yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—161no—
808C2C31×#243011yescharacteristic
809C2C31×#300511yescharacteristic
810C2C31×#300811yescharacteristic
811C2C31×#330911yescharacteristic
812C2C31×#332211yescharacteristic
813C2C31×#334711yescharacteristic
814C2C31×#335511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C31×#553C2semidirect
2. C2×C31×#480C2semidirect
3. C2×C31×#469C2semidirect
4. C31×#2414C2semidirect
5. C31×#2059C2semidirect
6. C31×#2033C2semidirect
7. C31×#2025C2semidirect
8. C31×#1999C2semidirect
9. C31×#1879C2semidirect
10. C31×#1875C2semidirect
11. C31×#1875C2semidirect
12. C31×#1870C2semidirect
13. C31×#1862C2semidirect
14. C31×#1854C2semidirect
15. C31×#1736C2semidirect
96. C31×#121D4semidirect
112. C2×C4⋊C4×C31D4semidirect
255. #25553C31direct (N × H)
348. C2×#553C2×C31semidirect
349. C2×#480C2×C31semidirect
350. C2×#469C2×C31semidirect
351. #2414C2×C31semidirect
352. #2059C2×C31semidirect
353. #2033C2×C31semidirect
354. #2025C2×C31semidirect
355. #1999C2×C31semidirect
356. #1879C2×C31semidirect
357. #1875C2×C31semidirect
358. #1875C2×C31semidirect
359. #1870C2×C31semidirect
360. #1862C2×C31semidirect
361. #1854C2×C31semidirect
362. #1736C2×C31semidirect
503. #121D4×C31semidirect
519. C2×C4⋊C4D4×C31semidirect
555. C31#25553direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C31×#5532
C2×C31×#4802
C2×C31×#4692
C31×#24142
C31×#20592
C31×#20332
C31×#20252
C31×#19992
C31×#18792
C31×#18752
C31×#18702
C31×#18622
C31×#18542
C31×#17362
#2555331